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discrete distribution is the distribution that can use the value of a whole number only while continuous distribution is the distribution that can assume any value between two numbers.
We'll assume reasonably that you get a correct answer with probability 0.5. Then the context implies that the number of correct answers is a sum of 12 Bernoulli random variables with p=0.5, which becomes a Binomial distribution with n=12 and p=0.5. Formally: Y(i)~Ber(0.5) => X = Y(1) + ... + Y(12) => X~Bin(12,0.5) The mean for a Binomial distribution is n*p, hence E(X)=12*0.5=6. The variance for a Binomial distribution is n*p*(1-p), hence Var(X)=12*0.5*0.5=3. The standard deviation is calculated as the square root of the variance so SD(X)=3^0.5=1.732.
In general you cannot. You will need to know more about the distribution of the variable - you cannot assume that the distribution is uniform or Normal.
Subjective If you assume particular events will happen with a certain prior distribution, that is Bayesian probability.
Contrast is a synonym for difference. Expected means when something can be easily predicted or you could assume this would happen. Reality is when is something that could happen but doesn't really include predicting anything. It is more of using common sense to analyze something that could happen.
The answer will depend on the underlying distribution for the variable. You may not simply assume that the distribution is normal.
discrete distribution is the distribution that can use the value of a whole number only while continuous distribution is the distribution that can assume any value between two numbers.
We'll assume reasonably that you get a correct answer with probability 0.5. Then the context implies that the number of correct answers is a sum of 12 Bernoulli random variables with p=0.5, which becomes a Binomial distribution with n=12 and p=0.5. Formally: Y(i)~Ber(0.5) => X = Y(1) + ... + Y(12) => X~Bin(12,0.5) The mean for a Binomial distribution is n*p, hence E(X)=12*0.5=6. The variance for a Binomial distribution is n*p*(1-p), hence Var(X)=12*0.5*0.5=3. The standard deviation is calculated as the square root of the variance so SD(X)=3^0.5=1.732.
There is no direct opposite for the noun experiment (testing). However, the verb experiment could have the opposite words "assume" or "accept" (without experiment).
I would assume you meant "The Angel experiment..."It had suspense, humor, and it had good content... awesome book!
If you assume a binomial distribution, the variance is n*p*(1-p) where n is the number of voters = 30 p is the probability of support = 0.36 So variance = 30*0.36*0.64 = 6.912
If we assume that the probability of an event occurring is 1 in 4 and that the event occurs to each individual independently, then the probability of the event occurring to one individual is 0.3955. In order to find this probability, we can make a random variable X which follows a Binomial distribution with 5 trials and probability of success 0.25. This makes sense because each trial is independent, the probability of success stays constant for each trial, and there are only two outcomes for each trial. Now you can find the probability by plugging into the probability mass function of the binomial distribution.
If the distribution is positively skewed distribution, the mean will always be the highest estimate of central tendency and the mode will always be the lowest estimate of central tendency. This is true if we assume the distribution has a single mode.
In general you cannot. You will need to know more about the distribution of the variable - you cannot assume that the distribution is uniform or Normal.
Prediction and hypothesis are kinda the same thing. Experiment is what you do to test your hypothesis or prediction.
I will assume that you are asking about probability distribution functions. There are two types: discrete and continuous. Some might argue that a third type exists, which is a mix of discrete and continuous distributions. When representing discrete random variables, the probability distribution is probability mass function or "pmf." For continuous distributions, the theoretical distribution is the probability density function or "pdf." Some textbooks will call pmf's as discrete probability distributions. Common pmf's are binomial, multinomial, uniform discrete and Poisson. Common pdf's are the uniform, normal, log-normal, and exponential. Two common pdf's used in sample size, hypothesis testing and confidence intervals are the "t distribution" and the chi-square. Finally, the F distribution is used in more advanced hypothesis testing and regression.
True. The rotation curve of galaxies typically shows that stars beyond the sun are moving faster than expected based on the visible mass distribution in the galaxy. This discrepancy suggests the presence of dark matter, which exerts gravitational influence on the stars and affects their motion.